Salah also became the first Reds player to score in each of their first six home matches at the start of a season.
He broke the deadlock with a calm finish into the far corner as half-time approached, and headed in a Kostas Tsimikas, Liverpool's defender, cross on the hour mark.
Here are the African headline-makers in the major European leagues:
Mohamed Salah (Liverpool)
Only Manchester City's 13-goal Erling Haaland has scored more in the Premier League this season than Salah, who raised his tally to 10.
"Exceptional, just exceptional player. Played a super game today and we all know how difficult it is against these tall centre-backs," said Liverpool boss Jurgen Klopp.
Nicolas Jackson (Chelsea)
The Senegal striker once again answered his critics with a crucial goal in an incredible 4-4 draw against Manchester City. Jackson has come under fire after a difficult start at Stamford Bridge following a close-season move from Villarreal, but he made it four goals in two games with a second-half finish against champions City. Fresh from a hat-trick in a win at Tottenham, Jackson netted after City goalkeeper Ederson spilled a shot.
Idrissa Gueye (Everton)
The Senegal midfielder scored a late winner to give Sean Dyche's side a 3-2 victory at Crystal Palace. Gueye kept his cool to fire home with four minutes to go, taking Abdoulaye Doucoure's pass in his stride and evading Tyrick Mitchell's challenge before drilling past Palace goalkeeper Sam Johnstone. Mali midfielder Doucoure had scored for Everton earlier.
Jonathan Bamba (Celta Vigo)
A brilliant strike by the Ivory Coast winger was not enough to lift Celta Vigo out of the relegation zone or take any points from a thrilling 4-3 defeat at Athletic Bilbao. Bamba lashed home from the edge of the box to put Celta 2-1 up, but his team were unable to capitalise.
Eric Maxim Choupo-Moting (Bayern Munich)
The Cameroon forward rose superbly to head in Bayern's fourth goal in a hard-fought 4-2 win against Heidenheim at the Allianz Arena. His goal came after Harry Kane scored twice and Raphael Guerreiro also netted in a game in which the promoted side hit back to level the scores at 2-2 before the German champions asserted themselves. With two goals in 10 appearances this season, Choupo-Moting is showing that despite the arrival of the superbly in-form Kane from Tottenham, he can still contribute important goals at the age of 34.
Serhou Guirassy (Stuttgart)
Stuttgart's Guirassy celebrated his return after an injury in style, scoring a late penalty to help beat lethargic Borussia Dortmund 2-1. The Guinean came off the bench and converted a spot-kick with seven minutes remaining to lift his side to third. Guirassy now has 15 goals in nine games this season. Kane has 17 in 11.
Nathan Tella (Bayer Leverkusen)
Tella scored his first league goal for Leverkusen in a 4-0 thrashing of Union Berlin. He made the most of a counter-attack just two minutes after coming on to score Bayer's fourth. England-born Tella said that being included in the Nigeria squad for World Cup qualifiers against Lesotho and Zimbabwe this month "fulfilled a dream".